Multilinear estimates and well‐posedness for the vortex filament fourth‐order Schrödinger equations | Zendy

Zhang Junyong | Zendy; Zheng Jiqiang | Zendy

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Multilinear estimates and well‐posedness for the vortex filament fourth‐order Schrödinger equations

Author(s) -

Zhang Junyong,

Zheng Jiqiang

Publication year - 2012

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.2684

Subject(s) - multilinear map , mathematics , nonlinear schrödinger equation , nonlinear system , initial value problem , norm (philosophy) , multiplier (economics) , vortex , schrödinger's cat , mathematical analysis , order (exchange) , schrödinger equation , mathematical physics , pure mathematics , physics , law , quantum mechanics , meteorology , finance , political science , economics , macroeconomics

This paper is concerned with the initial value problem for the fourth‐order nonlinear Schrödinger type equation related to the theory of vortex filament. By deriving a fundamental estimate on dyadic blocks for the fourth‐order Schrödinger through the [ k , Z ]‐multiplier norm method. we establish multilinear estimates for this nonlinear fourth‐order Schrödinger type equation. The local well‐posedness for initial data inH s( R ) with s > 1 ∕ 2 is implied by the multilinear estimates. Copyright © 2012 John Wiley & Sons, Ltd.

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